Topological link‐vertex analysis of the growth of purkinje cell dendritic trees in normal, reeler, and weaver mice

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Abstract
The growth of Purkinje cell dendritic trees in normal, reeler, and weaver mice has been defined by using Link‐Vertex Analysis. Growth probably occurs in three phases in normal and cortically located reeler trees. Phase I, completed by 7 days postnatum (dpn), establishes a rudimentary tree of 100 segments by random terminal branching. Phase II lasts from 7 to 20 dpn when some 690 and 450 segments are generated in normal and cortical reeler trees respectively. Phase II is initiated by an inductive stimulus mediated by a finite number of parallel fibres. Thereafter, dendritic trees develop a similar topology in normal and cortical reeler Purkinje cells through random interactions between parallel fibres and dendritic growth cones. We have defined this process with the aid of computer simulation techniques. Interactions appear to be restricted to a narrow growth front occupied by the highest centrifugally ordered terminals behind which adhesions occur at a greatly reduced frequency. The cortical reeler tree thus has fewer segments than normal because fewer parallel fibres are available, but it is surprisingly normal in most other respects. Phase III is a period of remodelling and extends from 20 dpn into adulthood when high‐ordered terminals are eroded and middle‐ordered terminals are added, with no change in total segment number in both normal and cortical reeler trees. Weaver and deeply placed reeler Purkinje cell dendritic trees are not influenced by parallel fibres. Accordingly, their growth is arrested at the end of Phase I, when both types of mutant tree have generated 100 segments by unrestrained random terminal branching. In the absence of parallel fibres, Phase II is not induced and remodelling, characteristic of Phase III, does not occur.